If the price of kerosene be raised by 9%, find how much percent a house holder must reduce his consumption of kerosene so that not to increase his expenditurea)9%b)8.25%c)9.05%d)9.25%Correct answer is option 'B'. Can you explain this answer?

Question

Answer

If the price of a commodity increases by R%, then the reduction in consumption. So as not to increase the expenditure is

= 8.25%

Answer

Understanding the Problem
When the price of kerosene increases by 9%, a household must reduce their consumption to maintain the same expenditure level. To find the percentage reduction in consumption, we can use a simple formula based on the relationship between price, consumption, and expenditure.
Key Formulas
- Let the original price of kerosene be P.
- Let the original quantity consumed be Q.
- The original expenditure (E) is given by:
E = P × Q
- After a 9% increase, the new price (P') becomes:
P' = P × (1 + 0.09) = 1.09P
- Let the new quantity consumed be Q'. The new expenditure must remain the same:
E = P' × Q'
Therefore,
P × Q = 1.09P × Q'
Setting Up the Equation
Since the expenditures are equal, we can simplify:
Q = 1.09 × Q'
To find Q', we rearrange the equation:
Q' = Q / 1.09
Calculating Percentage Reduction
The reduction in consumption is:
Reduction = Q - Q'
= Q - (Q / 1.09)
= Q × (1 - 1/1.09)
= Q × (1 - 0.917)
= Q × 0.0833 (approximately)
Now to find the percentage reduction:
Percentage Reduction = (Reduction / Q) × 100
= 0.0833 × 100
≈ 8.33%
Thus, rounding off, the household must reduce their consumption by approximately 8.25%, which matches option B.
Conclusion
To avoid increasing expenditure after a 9% price hike, a household must reduce kerosene consumption by about 8.25%.

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